Let Omega be an open bounded subset of Rn and f a continuous function on Omega satisfying f(x) > 0 for all x is an element of Omega. We consider the maximization problem for the integral fOmega f(x)u(x) dx over all Lipschitz continuous functions u subject to the Dirichlet boundary condition u = 0 on partial derivativeOmega and to the gradient constraint of the form H(Du(x)) less than or equal to 1, and prove that the supremum is 'achieved' by the viscosity solution of H(Du(x)) = 1 in Omega and u = 0 on partial derivativeOmega, where H denotes the convex envelope of H. This result is applied to an asymptotic problem, as p --> infinity, for quasi-minimizers of the integral integral(Omega)[1/p H(Du(x))(p) - f(x)u(x)] dx. An asymptotic problem as k --> infinity for inf integral(Omega)[k dist(Du(x),K) - f(x)u(x)] dx is also considered, where the infimum is taken all over u is an element of W-0(1,1)(Omega) and the set K is given by {xi H (xi) less than or equal to 1}.
Relaxation in an L-infinity-optimization problem / H., Ishii; Loreti, Paola. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 133(2003), pp. 599-615. [10.1017/s0308210500002559]
Scheda prodotto non validato
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo
Titolo: | Relaxation in an L-infinity-optimization problem | |
Autori: | ||
Data di pubblicazione: | 2003 | |
Rivista: | ||
Citazione: | Relaxation in an L-infinity-optimization problem / H., Ishii; Loreti, Paola. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 133(2003), pp. 599-615. [10.1017/s0308210500002559] | |
Handle: | http://hdl.handle.net/11573/14210 | |
Appartiene alla tipologia: | 01a Articolo in rivista |